Tension Force Estimation of Extradosed Bridge Cables Oscillating Nonlinearly under Gravity Effects

Abstract

Extradosed bridges have loose and sagged cables that are different from those used in cable-stayed bridges. The total tension force of an extradosed bridge cable estimated using the existing formulas is not accurate. Although the existing formulas are widely used in the field, they do not consider the exact deflection curve, features of nonlinear oscillation, and stretching force due to self-weight. In this study, a new method was developed to calculate the total tension force of the cable. In the new method, the total tension force of the cable includes the applied axial load and the stretching force due to self-weight. For the exact estimation of the applied axial load to the cable, the vibration of the cable was treated as a conservative nonlinear oscillation system, and a new formula was derived using the perturbation technique. The new formula was used to clearly explain the hardening effect due to the initial amplitude of the initial excitation, the presence of imaginary number of frequencies, the correlation with the stretching force due to self-weight, and the softening effect of the slenderness ratio on nonlinear natural frequency. For calculating the stretching force due to self-weight, the stretching of the cable for the static deformation was considered. A field test showed that it is necessary to add the stretching force due to self-weight to the estimated axial load for extradosed bridge cables and that the new method can be used to calculate the total tension force of loose and sagged cables.